Method and system for quantization for a general beamforming matrix in feedback information

ABSTRACT

Aspects of a method and system for utilizing Givens rotation expressions for quantization for a general beamforming matrix in feedback information. In one aspect of the invention, feedback information is computed at the receiving MIMO wireless device based on a geometric mean decomposition (GMD) method. The feedback information may include a matrix that describes a wireless medium. The matrix may represent a multiplicative product of at least one rotation matrix and at least one diagonal phase rotation matrix. Each of the rotation matrices may include at least one matrix element whose value is based on Givens rotation angle. The transmitting MIMO wireless device may subsequently transmit a plurality of signals via the wireless medium based on the received matrix information. The signal strength and/or signal to noise ratio (SNR) measurement (as measured in decibels, for example) associated with each of the transmitted plurality of signals may be about equal.

CROSS-REFERENCE TO RELATED APPLICATIONS/INCORPORATION BY REFERENCE

This application makes reference to, claims priority to, and claims thebenefit of U.S. Provisional Application Ser. No. 60/757,273 filed Jan.9, 2006.

This application also makes reference to:

-   U.S. patent application Ser. No. 11/327,690 filed on Jan. 6, 2006;-   U.S. patent application Ser. No. 11/327,752 filed on Jan. 6, 2006;    and-   U.S. application Ser. No. 11/052,389 filed Feb. 7, 2005.

Each of the above stated applications is hereby incorporated herein byreference in its entirety.

FIELD OF THE INVENTION

Certain embodiments of the invention relate to wireless communication.More specifically, certain embodiments of the invention relate to amethod and system for quantization for a general beamforming matrix infeedback information.

BACKGROUND OF THE INVENTION

Multiple input multiple output (MIMO) systems are wirelesscommunications systems that are specified in resolution 802.11 from theInstitute of Electrical and Electronics Engineers (IEEE). A MIMO systemthat receives a signal Y may compute a channel estimate matrix, H, basedon the received signal. The signal may comprise information generatedfrom a plurality of information sources. Each such information sourcemay be referred to as a spatial stream. A transmitting MIMO system mayutilize a plurality of transmitting antennas when transmitting thesignal Y. A receiving MIMO system may utilize a plurality of receivingantennas when receiving the signal Y. The channel estimate matrix for adownlink RF channel, H_(down), may describe a characteristic of thewireless transmission medium in the transmission path from atransmitter, to a receiver. The channel estimate for an uplink RFchannel, H_(up), may describe a characteristic of the wirelesstransmission medium in the transmission path from the receiver to thetransmitter.

According to the principle of reciprocity, a characteristic of thewireless transmission medium in the transmission path from thetransmitter to the receiver may be assumed to be identical to acorresponding characteristic of the wireless transmission medium in thetransmission path from the receiver to the transmitter. However, thechannel estimate matrix H_(down) may not be equal to a correspondingchannel estimate matrix for an uplink RF channel H_(up). For example, anoise level, for example an ambient noise level, in the vicinity of thetransmitter may differ from a noise level in the vicinity of thereceiver. Similarly, an interference level, for example electro-magneticinterference due to other electro-magnetic devices, in the vicinity ofthe transmitter may differ from an interference level in the vicinity ofthe receiver. At a transmitter, or receiver, there may also beelectrical cross-coupling, for example leakage currents, betweencircuitry associated with a receiving antenna, or a transmittingantenna, and circuitry associated with another receiving antenna, oranother transmitting antenna.

The principle of reciprocity, wherein it may be assumed thatH_(up)=H_(down), may also be based on the assumption that specificantennas at a transmitter or receiver are assigned for use astransmitting antennas, and/or assigned for use as receiving antennas. Atthe transmitter, a number of receiving antennas, N_(RX), utilized at thereceiver may be assumed. At the receiver, a number of transmittingantennas, N_(TX), utilized at the transmitter may be assumed. If theassignments of at least a portion of the antennas at the transmitter arechanged, the corresponding channel estimate matrix H′_(up) may not beequal H_(down). Similarly, if the assignments of at least a portion ofthe antennas at the receiver are changed, the corresponding channelestimate matrix H′_(down) may not be equal H_(up). Consequently, afterreassignment of antennas at the transmitter and/or receiver, theprinciple of reciprocity may not be utilized to characterizecommunications between the transmitter and the receiver when H_(up) doesnot equal H′_(down), when H′_(up) does not equal H_(down), or whenH′_(up) does not equal H′_(down).

The principle of reciprocity may enable a receiving wireless local areanetwork (WLAN) device A to receive a signal Y from a transmitting WLANdevice B, and to estimate a channel estimate matrix H_(down) for thetransmission path from the transmitting WLAN device B to the receivingWLAN device A. Based on the channel estimate matrix H_(down), the WLANdevice A may transmit a subsequent signal Y, via an uplink RF channel,to the WLAN device B based on the assumption that the channel estimatematrix H_(up) for the transmission path from the transmitting WLANdevice A to the receiving WLAN device B may be characterized by therelationship H_(up)=H_(down). When the WLAN devices A and B are MIMOsystems, corresponding beamforming matrices may be configured andutilized for transmitting and/or receiving signals at each WLAN device.

Beamforming is a method for signal processing that may allow atransmitting MIMO system to combine a plurality of spatial streams in atransmitted signal Y. Beamforming is also a method for signal processingthat may allow a receiving MMO system to separate individual spatialstreams in a received signal Y.

As a result of a failure of an assumed condition for the principle ofreciprocity, a beamforming matrix at the transmitting WLAN device,and/or a beamforming matrix at the receiving WLAN device, may beconfigured incorrectly. In a transmitted signal Y, from the perspectiveof a signal associated with an i^(th) spatial stream, a signalassociated with a j^(th) spatial stream may represent interference ornoise. Incorrect configuration of one or more beamforming matrices mayreduce the ability of the receiving WLAN device to cancel interferencebetween an i^(th) spatial stream and a j^(th) spatial stream.Consequently, the received signal Y may be characterized by reducedsignal to noise ratios (SNR). There may also be an elevated packet errorrate (PER) when the receiving WLAN device decodes information containedin the received signal Y. This may, in turn, result in a reducedinformation transfer rate, as measured in bits/second, forcommunications between the transmitting WLAN device and the receivingWLAN device.

In some MIMO systems, a transmitting WLAN device may transmit aplurality of spatial streams based on channel state information at thetransmitter (CSIT). The CSIT may be based on feedback information sentfrom the receiving WLAN device B to the transmitting WLAN device A.Based on the CSIT, the transmitting WLAN device A may compute estimatedvalues for the channel estimate matrix H_(down).

In a typical MIMO system, the transmitting WLAN device A may transmit aplurality of information bits simultaneously via the plurality oftransmitting antennas. The transmitting WLAN device A may allocate aportion of the plurality of information bits for transmission via atleast a portion of the plurality of transmitting antennas. Eachallocated portion of information bits may be error correction coded toenable the receiving WLAN device B to correctly detect the binary valuesassociated with each of the transmitted information bits in a receivedsignal. A received bit for which the receiving WLAN device detects anincorrect binary value may be referred to as a bit error. The rate, asmeasured over a time duration at which bit errors occur, may be referredto as a bit error rate (BER).

In some MIMO systems, the spatial streams transmitted by thetransmitting WLAN device A may be characterized by the bit error rate.An error correction coding method may be characterized by the number oferror correction bits that are transmitted with a given number ofinformation bits. The ratio of information bits to the total number oferror correction and information bits may be referred to as a codingrate. Spatial streams that are transmitted by a transmitting WLAN deviceA utilizing larger values for the coding rate, may be associated withhigher BERs at the receiving WLAN device B in comparison to spatialstreams that are transmitted utilizing smaller values for the codingrate. A larger value for the coding rate may be referred to as a weakcoding rate in comparison to a smaller value of the coding rate. Theerror correction coding may enable the receiving WLAN device B to reducethe BER.

In some MIMO systems that utilize CSIT, the signal strength and/orsignal to noise ratio (SNR) may vary among the transmitted spatialstreams. In such MIMO systems that utilize higher, or weaker, codingrates, the BER performance may not be acceptable.

Further limitations and disadvantages of conventional and traditionalapproaches will become apparent to one of skill in the art, throughcomparison of such systems with some aspects of the present invention asset forth in the remainder of the present application with reference tothe drawings.

BRIEF SUMMARY OF THE INVENTION

A system and/or method for utilizing Givens rotation expressions forquantization for a general beamforming matrix in feedback information,substantially as shown in and/or described in connection with at leastone of the figures, as set forth more completely in the claims.

These and other advantages, aspects and novel features of the presentinvention, as well as details of an illustrated embodiment thereof, willbe more fully understood from the following description and drawings.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a block diagram of an exemplary system for wireless datacommunications, which may be utilized in connection with an embodimentof the invention.

FIG. 2 is a block diagram of an exemplary MIMO system that may beutilized in connection with an embodiment of the invention.

FIG. 3A is an exemplary diagram illustrating beamforming that may beutilized in connection with an embodiment of the invention.

FIG. 3B is an exemplary diagram illustrating channel feedback, which maybe utilized in connection with an embodiment of the invention.

FIG. 3C is an exemplary diagram illustrating a system for GMDbeamforming, in accordance with an embodiment of the invention.

FIG. 3D is an exemplary diagram illustrating a system for GMDbeamforming with decoding, in accordance with an embodiment of theinvention.

FIG. 4 is an exemplary functional block diagram of transceivercomprising a transmitter and a receiver in a MIMO system, which may beutilized in accordance with an embodiment of the invention.

FIG. 5 is a flowchart illustrating exemplary steps for computingquantization for a general beamforming matrix in feedback information,in accordance with an embodiment of the invention.

FIG. 6 is a flowchart illustrating exemplary steps for utilizingquantization for a general beamforming matrix in feedback information,in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Certain embodiments of the invention relate to a method and system forquantization for a general beamforming matrix in feedback information.Various embodiments of the invention may be utilized to enablecommunications within wireless communications systems between atransmitting multiple input multiple output (MIMO) wireless device and areceiving MIMO wireless device. In one aspect of the invention, feedbackinformation may be computed at the receiving MIMO wireless device basedon signals received from the transmitting MIMO wireless device. Any of aplurality of beamforming methods, for example geometric meandecomposition (GMD) or singular value decomposition (SVD), may beutilized. The feedback information may comprise a matrix that describesa wireless medium. The matrix may represent a multiplicative product ofat least one rotation matrix and at least one diagonal phase rotationmatrix. Each of the rotation matrices may comprise at least one matrixelement whose value is based on Givens rotation angle. The transmittingMIMO wireless device may subsequently transmit a plurality of signalsvia the wireless medium based on the received matrix information. Thesignal strength and/or signal to noise ratio (SNR) measurement (asmeasured in decibels, for example) associated with each of thetransmitted plurality of signals may be about equal.

Various embodiments of the invention may exhibit improved bit error rateperformance (BER) when utilizing weaker coding rates when compared tosome conventional MIMO systems. As a result of improved BER performance,various embodiments of the invention may also enable higher informationtransfer rates between a transmitting MIMO wireless device and areceiving MIMO wireless device via a wireless medium.

Givens matrices may be utilized to reduce a quantity of informationcommunicated in feedback information via an uplink RF channel. Thefeedback information may comprise specifications for a feedbackbeamforming matrix that may be utilized when transmitting signals via acorresponding downlink RF channel. The feedback beamforming matrix mayrepresent a rotated version of an un-rotated beamforming matrix. TheGivens matrices may be utilized to apply one or more Givens rotations toun-rotated beamforming matrix. The feedback beamforming matrix may becomputed based on a matrix product of a plurality of Givens matrices.The feedback beamforming matrix may comprise comparable informationcontent to the un-rotated beamforming matrix. The feedback beamformingmatrix may be encoded utilizing fewer bits than may be required toencode the un-rotated beamforming matrix. Various embodiments of theinvention may be utilized in wireless communications systems, includingwireless data communications systems.

Feedback information may be utilized to reduce the likelihood thatsignals Y will be transmitted incorrectly during beamforming. Feedbackcomprises a mechanism by which a receiving WLAN device A may compute achannel estimate matrix H_(down). The computed channel estimate matrixmay be utilized to compute feedback information that may be utilized bythe WLAN device B to configure a beamforming matrix associated with thedownlink RF channel. The feedback information may be communicated fromthe WLAN device A to the WLAN device B via the uplink RF channel. Thefeedback information may comprise a full description of the downlink RFchannel. A full description of the downlink RF channel may comprise afrequency channel estimate for each subcarrier frequency associated witheach spatial stream contained in the downlink RF channel. Each frequencychannel estimate may be characterized in a Cartesian coordinate format,or in a polar coordinate format. In the Cartesian coordinate format,each frequency channel estimate may be represented as an in-phase (I)amplitude component, and a quadrature (Q) phase amplitude component. Inthe polar coordinate format, each frequency channel estimate may berepresented as a magnitude (ρ) component, and an angle (θ) component.

In some conventional systems, a large quantity of feedback informationmay be communicated in the feedback direction. RF channel bandwidth thatis dedicated for use in communicating feedback information may reducethe quantity of other types of information that may be communicatedbetween the WLAN device A and the WLAN device B within a given timeinterval. The feedback information may be referred to as overhead withinthe uplink RF channel. The overhead may reduce the information transferrate between the WLAN device A and the WLAN device B associated withnon-feedback information.

FIG. 1 is a block diagram of an exemplary system for wireless datacommunications, which may be utilized in connection with an embodimentof the invention. With reference to FIG. 1, there is shown adistribution system (DS) 110, an extended service set (ESS) 120, and anIEEE 802.x LAN 122. The ESS 120 may comprise a first basic service set(BSS) 102, and a second BSS 112. The first BSS 102 may comprise a first802.11 WLAN station 104, a second 802.11 WLAN station 106, and an accesspoint (AP) 108. The second BSS 112 may comprise a first 802.11 WLANstation 114, a second 802.11 WLAN station 116, and an access point (AP)118. The IEEE 802 LAN 122 may comprise a LAN station 124, and a portal126. An IEEE 802.11 WLAN station, or IEEE 802.11 WLAN device, is a WLANsystem that may be compliant with at least a portion of the IEEE 802.11standard.

A WLAN is a communications networking environment that comprises aplurality of WLAN devices that may communicate wirelessly via one ormore uplink and/or downlink RF channels. The BSS 102 or 112 may be partof an IEEE 802.11 WLAN that comprises at least 2 IEEE 802.11 WLANstations, for example, the first 802.11 WLAN station 104, the second802.11 WLAN station 106, and the AP 108, which may be members of the BSS102. Non-AP stations within BSS 102, the first 802.11 WLAN station 104,and the second 802.11 WLAN station 106, may individually form anassociation with the AP 108. An AP, such as AP 108, may be implementedas an Ethernet switch, bridge, or other device in a WLAN, for example.Similarly, non-AP stations within BSS 112, the first 802.11 WLAN station114, and the second 802.11 WLAN station 116, may individually form anassociation with the AP 118. Once an association has been formed betweena first 802.11 WLAN station 104 and an AP 108, the AP 108 maycommunicate reachability information about the first 802.11 WLAN station104 to other APs associated with the ESS 120, such as AP 118, andportals such as the portal 126. The WLAN station 104 may subsequentlycommunicate information wirelessly via the BSS 102. In turn, the AP 118may communicate reachability information about the first 802.11 WLANstation 104 to stations in BSS 112. The portal 126, which may beimplemented as, for example, an Ethernet switch or other device in aLAN, may communicate reachability information about the first 802.11WLAN station 104 to stations in LAN 122 such as the 802 LAN station 124.The communication of reachability information about the first 802.11WLAN station 104 may enable WLAN stations that are not in BSS 102, butare associated with ESS 120, to communicate wirelessly with the first802.11 WLAN station 104.

The DS 110 may provide an infrastructure which enables a first 802.11WLAN station 104 in one BSS 102, to communicate wirelessly with a first802.11 WLAN station 114 in another BSS 112. The DS 110 may also enable afirst 802.11 WLAN station 104 in one BSS 102 to communicate with an 802LAN station 124 in an IEEE 802 LAN 122, implemented as, for example awired LAN. The AP 108, AP 118, or portal 126 may provide a means bywhich a station in a BSS 102, BSS 112, or LAN 122 may communicateinformation via the DS 110. The first 802.11 WLAN station 104 in BSS 102may communicate information wirelessly to a first 802.11 WLAN station114 in BSS 112 by transmitting the information wirelessly to AP 108,which may transmit the information via the DS 110 to AP 118, which inturn may transmit the information wirelessly to station 114 in BSS 112.The first 802.11 WLAN station 104 may communicate information wirelesslyto the 802 LAN station 124 in LAN 122 by transmitting the informationwirelessly to AP 108, which may transmit the information via the DS 110to the portal 126, which in turn may transmit the information to the 802LAN station 124 in LAN 122. The DS 110 may utilize wirelesscommunications via an RF channel, wired communications, such as IEEE 802Ethernet, or a combination thereof.

A WLAN station or AP may utilize one or more transmitting antennas, andone or more receiving antennas when communicating information. A WLANstation or AP that utilizes a plurality of transmitting antennas and/ora plurality of receiving antennas may be referred to as a multiple inputmultiple output (MIMO) system.

FIG. 2 is a block diagram of an exemplary MIMO system that may beutilized in connection with an embodiment of the invention. Withreference to FIG. 2 there is shown a baseband processor 272, atransceiver 274, an RF front end 280, a plurality of receiving antennas276 a, . . . , 276 n, and a plurality of transmitting antennas 278 a, .. . , 278 n. The transceiver 274 may comprise a processor 282, areceiver 284, and a transmitter 286.

The processor 282 may perform digital receiver and/or transmitterfunctions in accordance with applicable communications standards. Thesefunctions may comprise, but are not limited to, tasks performed at lowerlayers in a relevant protocol reference model. These tasks may furthercomprise the physical layer convergence procedure (PLCP), physicalmedium dependent (PMD) functions, and associated layer managementfunctions. The baseband processor 272 may perform functions inaccordance with applicable communications standards. These functions maycomprise, but are not limited to, tasks related to analysis of datareceived via the receiver 284, and tasks related to generating data tobe transmitted via the transmitter 286. These tasks may further comprisemedium access control (MAC) layer functions as specified by pertinentstandards.

The receiver 284 may perform digital receiver functions that maycomprise, but are not limited to, fast Fourier transform processing,beamforming processing, equalization, demapping, demodulation control,deinterleaving, depuncture, and decoding. The transmitter 286 mayperform digital transmitter functions that comprise, but are not limitedto, coding, puncture, interleaving, mapping, modulation control, inversefast Fourier transform processing, beamforming processing. The RF frontend 280 may receive analog RF signals via antennas 276 a, . . . , 276 n,converting the RF signal to baseband and generating a digital equivalentof the received analog baseband signal. The digital representation maybe a complex quantity comprising I and Q components. The RF front end280 may also transmit analog RF signals via an antenna 278 a, . . . ,278 n, converting a digital baseband signal to an analog RF signal.

In operation, the processor 282 may receive data from the receiver 284.The processor 282 may communicate received data to the basebandprocessor 272 for analysis and further processing. The basebandprocessor 272 may generate data to be transmitted via an RF channel bythe transmitter 286. The baseband processor 272 may communicate the datato the processor 282. The processor 282 may generate a plurality of bitsthat are communicated to the receiver 284. The processor 282 maygenerate signals to control the operation of the modulation process inthe transmitter 286, and of the demodulation process in the receiver284.

FIG. 3A is an exemplary diagram illustrating beamforming that may beutilized in connection with an embodiment of the invention. Referring toFIG. 3A there is shown a transmitting mobile terminal 302, a receivingmobile terminal 322, and a plurality of RF channels 342. Thetransmitting mobile terminal 302 comprises a transmit filter coefficientblock V 304, a first source signal s₁ 306, a second source signal s₂308, a third source signal s₃ 310, and a plurality of transmittingantenna 312, 314, and 316. The receiving mobile terminal 322 comprises areceive filter coefficient block U* 324, a first destination signal ŝ₁326, a second destination signal ŝ₂ 328, a third destination signal ŝ₃330, and a plurality of receiving antenna 332, 334, and 336. Anexemplary mobile terminal may be a WLAN station 104, for example. Acorresponding matrix V may be associated with the transmit filtercoefficient block V 304. A corresponding matrix U* may be associatedwith the receive filter coefficient block U* 324. The matrices V and U*may be utilized in connection with beamforming.

In operation, the transmitting antenna 312 may enable transmission of asignal x₁, the transmitting antenna 314 may enable transmission of asignal x₂, and the transmitting antenna 316 may enable transmission of asignal x₃. In a beamforming operation, each of the transmitted signalsx₁, x₂, and x₃ may be a function of a weighted summation of at least oneof the plurality of the source signals s₁, s₂, and s₃. The weights maybe determined by the beamforming V matrix such that:X=VS_(S)  equation[1a]where X may be a 3×1 vector representation of the transmitted signalsx₁, x₂, and x₃, for example:

$\begin{matrix}{X = \begin{bmatrix}x_{1} \\x_{2} \\x_{3}\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {1b} \right\rbrack}\end{matrix}$S_(S) may be a 3×1 vector representation of the source signals s₁, s₂,and s₃, for example:

$\begin{matrix}{S_{S} = \begin{bmatrix}s_{1} \\s_{2} \\s_{3}\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {1c} \right\rbrack}\end{matrix}$and V may be a 3×3 matrix representation of the beamforming V matrix,for example:

$\begin{matrix}{V = \begin{bmatrix}v_{11} & v_{12} & v_{13} \\v_{21} & v_{22} & v_{23} \\v_{31} & v_{32} & v_{33}\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {1d} \right\rbrack}\end{matrix}$

The receiving antenna 332 may receive a signal y₁, the receiving antenna334 may receive a signal y₂, and the receiving antenna 336 may receive asignal y₃. The plurality of RF channels 342 may be characterizedmathematically by a transfer coefficient matrix H. The transfercoefficient matrix H may also be referred to as a channel estimatematrix.

The plurality of received signals y₁, y₂, y₃, may be expressed as afunction of the plurality of transmitted signals x₁, x₂, x₃, and thetransfer coefficient matrix H in the following equation, for example:Y=HX+N  equation[2a]where Y may be a 3×1 vector representation of the received signals y₁,y₂, and y₃, for example:

$\begin{matrix}{Y = \begin{bmatrix}y_{1} \\y_{2} \\y_{3}\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {2b} \right\rbrack}\end{matrix}$H may be a 3×3 matrix representation of the transfer coefficient matrix,for example:

$\begin{matrix}{H = \begin{bmatrix}h_{11} & h_{12} & h_{13} \\h_{21} & h_{22} & h_{23} \\h_{31} & h_{32} & h_{33}\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {2c} \right\rbrack}\end{matrix}$and N may be a 3×1 vector representation of noise that may exist in thecommunications medium, for example:

$\begin{matrix}{N = \begin{bmatrix}n_{1} \\n_{2} \\n_{3}\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {2d} \right\rbrack}\end{matrix}$

When utilizing singular value decomposition (SVD), the matrix H fromequation[2a] may be represented as in the following equation:H={tilde under (U)}S{tilde under (V)}*  equation[3a]where {tilde under (U)} may represent a column orthogonal matrix, {tildeunder (V)}* may represent an Hermitian transpose of an orthogonal matrix{tilde under (V)}, and S may represent a diagonal matrix, for example.The matrix S may comprise a plurality of nonzero matrix diagonalelements, the values of which may correspond to at least a portion ofsingular values associated with the matrix H.

A matrix V may be represented according to the following equation:V={tilde under (V)}{tilde under (D)}  equation[3b]where {tilde under (D)} may represent a diagonal steering matrix. Thematrix V may represent a rotated version of the matrix {tilde under(V)}. Each of the rows within the matrix {tilde under (V)} may compriseone or more matrix elements that may each be represented as a complexnumber. The matrix may {tilde under (D)} rotate the matrix {tilde under(V)} such that the last row of the matrix V may comprise a correspondingnumber of matrix elements, each of which may be represented as a realnumber. The matrix V may be referred to as being phase invariant basedon the equation[3b].

A matrix U may be similarly represented by a matrix multiplicationproduct of the matrix {tilde under (U)}, and the steering matrix {tildeunder (D)}. The equation[3a] may be represented:H={tilde under (U)}{tilde under (D)}S {tilde under (D)}*{tilde under(V)}*  equation[4]

Various embodiments of the invention may utilize decomposition methodsother than SVD. The embodiments may include utilizing methods based ongeometric mean decomposition (GMD), for example. When utilizing GMD, thematrix S may be represented as in the following equation:S=QRP*  equation[5]where matrices Q and P may represent column orthogonal matrices, and thematrix R may represent an upper diagonal matrix. The matrix elementsassociated with the matrix R may each be represented as a real number.Values associated with each of the diagonal matrix elements in thematrix R may be equal such that r_(ii)=r_(jj), where r_(ii) mayrepresent an i^(th) diagonal matrix element and r_(jj) may represent avalue associated with a j^(th) diagonal matrix element. The valueassociated with a diagonal matrix element may be about equal to ageometric mean value for at least a portion of the singular valuesassociated with the matrix S. When utilizing GMD, one representation ofthe equation[3a] may be as shown in the following equation:H={tilde under (U)}Q{tilde under (D)}R{tilde under (D)}*P*{tilde under(V)}*  equation[6a]where the beamforming V matrix may be defined:V={tilde under (V)} P{tilde under (D)}  equation[6b]and the beamforming U matrix may be defined:U={tilde under (U)}Q{tilde under (D)}  equation[6c]

In the equation[6a], the matrix S, from equation[3a] may be equal to thematrix multiplication product Q{tilde under (D)}R{tilde under (D)}*P*.This product may further be represented as the matrix R, a matrixmultiplication product Q{tilde under (D)} and a matrix multiplicationproduct {tilde under (D)}*P*. The matrix multiplication product {tildeunder (D)}*P* may represent a rotated version of the matrix P*. However,the matrix P, as represented in equations [5] and [6a], may not possessa property of phase invariance that would ensure that a matrix computedbased on the matrix multiplication product {tilde under (D)}R{tildeunder (D)}* is a real-valued matrix. Consequently, the matrix computedbased on the matrix multiplication product {tilde under (D)}R{tildeunder (D)}* from equation[6a] may comprise one or more matrix elements,the values of which may each be represented as a complex number.

When utilizing GMD, another representation of the equation[3a] may be asshown in the following equation:H={tilde under (U)}{tilde under (D)}QRP*{tilde under (D)}*{tilde under(V)}*  equation[6d]

In the equation[6d], the matrix H may be represented as a matrixmultiplication product of the matrix multiplication product QRP*, thematrix multiplication product {tilde under (U)}{tilde under (D)}, andthe matrix multiplication product {tilde under (D)}*{tilde under (V)}*.The matrix multiplication product {tilde under (D)}*{tilde under (V)}*may possess the phase invariant property as indicated in equation[3b].As a result, the matrix R in equation[6d] may comprise matrix elements,the values of which may each be represented as a real number.

Various metrics may be defined based on equation[6d]. One metric may bebased on the matrix multiplication product P*{tilde under (D)}*{tildeunder (V)}*. This metric may be utilized in connection with the matrix Vthis is associated with the transmit filter coefficient block V 304 asin the following equation:V={tilde under (V)}{tilde under (D)}P  equation[7a]where the matrix {tilde under (V)}{tilde under (D)}P may be derivedbased on the matrix multiplication product P*{tilde under (D)}*{tildeunder (V)}*.

Another metric may be based on the matrix multiplication product {tildeunder (U)}{tilde under (D)}Q This metric may be utilized in connectionwith the matrix U*, associated with the receive filter coefficient blockU* 324 as in the following equation:U*=Q*{tilde under (D)}*{tilde under (U)}*  equation[7b]where the matrix Q*{tilde under (D)}*{tilde under (U)}* may be derivedbased on the matrix multiplication product {tilde under (U)}{tilde under(D)}Q.

In various embodiments of the invention, the metric {tilde under(V)}{tilde under (D)}P may be utilized by a receiver 322 for sendingchannel feedback information to a transmitter 302. The metric {tildeunder (V)}{tilde under (D)}P may be computed based on the matrixmultiplication product P*{tilde under (D)}*{tilde under (V)}*. Thetransmitter 302 may utilize the feedback information when transmittingsubsequent signals to the receiver 322. Based on the matrix V, as inequation[7a], the transmitter 302 may transmit subsequent spatialstreams s₁, s₂, and s₃ such that the signals transmitted via thecorresponding transmitting antennas 312, 314, and 316 are eachcharacterized by approximately equal signal strength and/or SNRmeasurements. A signal strength and/or SNR may be measured in decibels(dB), for example. The metric {tilde under (U)}{tilde under (D)}Q may beutilized at the receiver 322 when receiving the subsequent signalstransmitted by the transmitter 302.

In a MIMO system that utilizes beamforming as shown in FIG. 3A, thevalues associated with the matrices V, H, and U* may be such that thevalue of the transmitted signal s_(i) may be approximately equal to thevalue of the corresponding received signal ŝ_(i), where the index i mayindicate an i^(th) spatial stream. In various embodiments of theinvention that utilize GMD, the matrix V, associated with the transmitfilter coefficient block V 304, may be computed based on the metric{tilde under (V)}{tilde under (D)}P, and the matrix U*, associated withthe receive filter coefficient block U* 324, may be computed based onthe metric {tilde under (U)}{tilde under (D)}Q as shown in equations[7a] and [7b]. The receiver 322 may compute a channel estimate,H_(down), for a downlink RF channel based on a received signal from thetransmitter 302. The transmitter 302 may compute a channel estimate,H_(up), for an uplink RF channel based on a received signal from thereceiver 322. The transmit filter coefficient block V 304 may set valuesassociated with the matrix V, utilized for communications via thedownlink RF channel, based on the channel estimate H_(up).

When the receiver 322 sends feedback information to the transmitter 302via the uplink RF channel, the receiver 322 may compute valuesassociated with a matrix V that may be based on the channel estimateH_(down). The receiver 322 may subsequently communicate the computedmatrix V to the transmitter 302 via the uplink RF channel. Thetransmitter 302 may subsequently set values associated with the matrixV, utilized for communications via the downlink RF channel, based on thechannel estimate H_(down).

FIG. 3B is an exemplary diagram illustrating channel feedback, which maybe utilized in connection with an embodiment of the invention. Referringto FIG. 3B, there is shown a transmitting mobile terminal 302, areceiving mobile terminal 322, and a communications medium 344. Thecommunications medium 344 may represent a wireless communicationsmedium. The transmitting mobile terminal 302 may transmit a signalvector X to the receiving mobile terminal 322 via the communicationsmedium 344. The communications direction from the transmitting mobileterminal 302 to the receiving mobile terminal 322 may be referred to asa downlink direction. The signal vector X may comprise a plurality ofspatial streams simultaneously transmitted via transmitting antennas312, 314 and 316, for example. The signal vector X may be beamformed bythe transmitting mobile terminal 302 based on a beamforming matrix V.The signal vector X may travel through the communications medium 344.The signal vector X may be altered while traveling through thecommunications medium 344. The transmission characteristics associatedwith the communications medium 344 may be characterized by a transferfunction H. The signal vector X may be altered based on the transferfunction H. In the downlink direction, the transfer function H may bereferred to as H_(down). The altered signal vector X may be representedas the signal Y. The receiving mobile terminal 322 may receive thesignal Y. The receiving mobile terminal 322 may determine one or morevalues associated with the transfer function H_(down) based on thesignal Y received via the communications medium 344.

The receiving mobile terminal 322 may compute one or more valuesassociated with a matrix V based on the information related to thetransfer function H_(down). The receiving mobile terminal 322 maycommunicate information related to the matrix V to the transmittingmobile terminal 302 as feedback information. The feedback information(H_(down)) may represent feedback information based on the informationrelated to the transfer function H_(down). The receiving mobile terminal322 may communicate the feedback information (H_(down)) via atransmitted signal vector X_(f). The transmitted signal vector X_(f) maybe transmitted to the transmitting mobile terminal 302 via thecommunications medium 344. The signal vector X_(f) may be altered whiletraveling through the communications medium 344. The communicationsdirection from the receiving mobile terminal 322 to the transmittingmobile terminal 302 may be referred to as an uplink direction. Thesignal vector X_(f) may be altered based on the transfer function H. Inthe uplink direction, the transfer function H may be referred to asH_(up). The altered signal vector X_(f) may be represented as the signalY_(f). The transmitting mobile terminal 302 may receive the signalY_(f).

The transmitting mobile terminal 302 may determine one or more valuesassociated with the transfer function H_(up) based on the signal Y_(f)received via the communications medium 344. The transmitting mobileterminal 302 may utilize the received feedback information (H_(down)) tobeamform subsequent signal vectors X, which may be transmitted in thedownlink direction from the transmitting mobile terminal 302 to thereceiving mobile terminal 322.

Various embodiments of the invention may reduce the quantity of feedbackinformation that may be communicated from the receiver 322 to thetransmitter 302 via the uplink RF channel. In one aspect of theinvention, the computed metric {tilde under (V)}{tilde under (D)}P maybe represented based on a product of Givens matrices:V=G ₁(ψ₁)G ₂(ψ₂)D ₁(φ₁,φ₂, . . . , φ_(N))  equation[8]where G_(j)(ψ_(j)) may represent a Givens matrix associated with arotation angle ψ_(j), and D₁(φ_(k)) may represent a diagonal matrix withphase shift angles φ_(k).

The feedback information communicated by the receiver 322 may compriseencoded rotation angles ψ_(j). The transmitter 302 may utilize theencoded rotation angles to reconstruct the matrix V based on thefeedback information.

FIG. 3C is an exemplary diagram illustrating a system for GMDbeamforming, in accordance with an embodiment of the invention.Referring to FIG. 3C there is shown a transmitting mobile terminal 302,a receiving mobile terminal 352, and a plurality of RF channels 342. Thetransmitting mobile terminal 302 comprises a transmit filter coefficientblock V 304, a first source signal s₁ 306, a second source signal s₂308, a third source signal s₃ 310, and a plurality of transmittingantenna 312, 314, and 316. The receiving mobile terminal 352 comprises areceive filter coefficient block U* 324, a plurality of receivingantenna 332, 334, and 336, a scaled slicer block 362, and a matrixsubtraction block 364.

The scaled slicer block 362 may enable detection of a received estimatedsignal ŝ_(i), where the index i may represent an i^(th) received signalamong a plurality of signals received simultaneously from thetransmitter 302. The scale factor utilized by the scaled slicer block362 may be based on a value associated with a diagonal matrix elementfrom the upper triangular matrix R. The matrix R may be defined as inconnection with equation[5]. The group of received signals ŝ_(i) may berepresented as a received signal vector Ŝ_(R). The matrix subtractionblock 364 may enable cancellation of a detected component signal ŝ_(i)from the signal vector Ŝ_(R). The matrix subtraction block 364 maysubtract a value corresponding to a diagonal matrix element r_(ii) fromthe upper triangular matrix R. The value associated with each diagonalmatrix element r_(ii) may be about equal.

An exemplary N×N upper triangular matrix R may be represented asfollows:

$\begin{matrix}{R = \begin{bmatrix}r_{11} & r_{12} & \ldots & \; & r_{1N} \\0 & r_{22} & r_{23} & \ldots & r_{2N} \\\vdots & \ddots & \ddots & \; & \vdots \\\; & \; & \; & \; & \; \\0 & \ldots & \; & 0 & r_{NN}\end{bmatrix}} & {{equation}\mspace{14mu}\lbrack 9\rbrack}\end{matrix}$

In operation, the receiving mobile terminal 352 may compute estimatesfor the individual destination signals, ŝ_(i), in the vector Ŝ_(R) basedon a zero forcing (ZF) approach. The loop comprising the scaled slicerblock 362, matrix subtraction block 364, and receive filter coefficientblock U* 324 may implement a solution for the individual destinationsignals based on ZF as in the following equation:Z=Ŷ−(R−diag(R))Ŝ _(R)  equation[10a]where the N×1 column vector Ŝ_(R), may be represented as follows:

$\begin{matrix}{{\hat{S}}_{R} = \begin{bmatrix}{\hat{s}}_{1} \\{\hat{s}}_{2} \\\vdots \\\; \\{\hat{s}}_{N}\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {10b} \right\rbrack}\end{matrix}$and where Z is an N×1 column vector generated based on ZF, and diag(T) aversion of the matrix T comprising the diagonal terms of the matrix T.The vector Ŷ may represent an N×1 column vector comprising a pluralityof signals generated by the receive filter coefficient block U* 324,which may be defined as in the following equation:Ŷ=U*Y  equation[11]where Y may be as defined in equation[2a], and U* may be defined as inequation[7b], for example.

When solving for each of the individual destination signals, ŝ_(i), thescaled slicer block 362 may compute estimated values for Q and Icomponents associated with the individual destination signal. For anexemplary 3×3 matrix R, and 3×1 vectors Z, Ŷ, and Ŝ_(R):

$\begin{matrix}{\begin{bmatrix}z_{1} \\z_{2} \\z_{3}\end{bmatrix} = {\begin{bmatrix}{\hat{y}}_{1} \\{\hat{y}}_{2} \\{\hat{y}}_{3}\end{bmatrix} - {\begin{bmatrix}0 & r_{12} & r_{13} \\0 & 0 & r_{23} \\0 & 0 & 0\end{bmatrix}\begin{bmatrix}{\hat{s}}_{1} \\{\hat{s}}_{2} \\{\hat{s}}_{3}\end{bmatrix}}}} & {{equation}\mspace{14mu}\left\lbrack {12a} \right\rbrack}\end{matrix}$where:z₃=ŷ₃  equation[12b]z ₂ =ŷ ₂ −r ₂₃ ŝ ₃  equation[12c]z ₁ =ŷ ₁ −r ₁₂ ŝ ₂ −r ₁₃ ŝ ₃  equation[12d]

By utilizing the scaled slicer block 362, an estimated value for theindividual destination signal, ŝ₃, may be computed based on the value z₃determined in equation[12b]. An estimated value for the individualdestination signal, ŝ₂, may be computed based on the value z₂ determinedin equation[12c]. The value z₂ may be computed based on the estimatedvalue for the individual destination signal, ŝ₃. An estimated value forthe individual destination signal, ŝ₁, may be computed based on thevalue z₁ determined in equation[12d]. The value z₁ may be computed basedon the estimated value for the individual destination signals, ŝ₂ andŝ₃.

FIG. 3D is an exemplary diagram illustrating a system for GMDbeamforming with decoding, in accordance with an embodiment of theinvention. Referring to FIG. 3D there is shown a transmitting mobileterminal 302, a receiving mobile terminal 372, and a plurality of RFchannels 342. The transmitting mobile terminal 302 comprises a transmitfilter coefficient block V 304, a first source signal s₁ 306, a secondsource signal s₂ 308, a third source signal s₃ 310, and a plurality oftransmitting antenna 312, 314, and 316. The receiving mobile terminal352 comprises a receive filter coefficient block U* 324, a plurality ofreceiving antenna 332, 334, and 336, a scaled slicer block 362, and amatrix subtraction block 364. The transmitting mobile terminal 302, andthe plurality of RF channels 342 may be substantially as described inFIG. 3C. The transmit filter coefficient block V 304, the first sourcesignal s₁ 306, the second source signal s₂ 308, the third source signals₃ 310, and the plurality of transmitting antenna 312, 314, and 316 maybe substantially as described in FIG. 3C. The receive filter coefficientblock U* 324, the plurality of receiving antenna 332, 334, and 336, thescaled slicer block 362, and the matrix subtraction block 364 may besubstantially as described in FIG. 3C. FIG. 3D also shows a demapperblock 374, a decoder block 376, an encoder block 378, and a mapper block380.

The demapper block 374 may enable transformation of a signal comprisingQ and I components to a point within a constellation map. The pointwithin the constellation map may correspond to a binary representationof the transformed signal. The transformation may be based on ademodulation technique. The binary representation may comprise encodedinformation.

The decoder block 376 may enable decoding of encoded information andsubsequent generation of binary information. The decoding may enable thedetection and/or correction of bit errors in the encoded informationwhen generating the binary information.

The encoder block 378 may enable encoding of binary information andsubsequent generation of encoded information.

The mapper block 380 may enable transformation of encoded informationinto a signal comprising Q and I components. The encoded information maybe transformed into a representation comprising one or more symbols,wherein each symbol may correspond, or map, to a point within aconstellation map. The symbols may be utilized to generate correspondingQ and I components. The transformation may be based on a modulationtechnique.

In operation, the receiving mobile terminal 372 may compute estimatesfor the individual destination signals, ŝ_(i), in the vector Ŝ_(R) basedon a zero forcing (ZF) approach. The loop comprising the scaled slicerblock 362, demapper block 374, decoder block 376, encoder block 378,mapper block 380, matrix subtraction block 364, and receive filtercoefficient block U* 324 may implement a solution for the individualdestination signals based on ZF as in equation[10a]. The mapper blockmay be utilized to generate a corresponding vector Ŝ_(R)′ based on thevector Ŝ_(R). The vector Ŝ_(R)′ may comprise individual signals ŝ_(i)′,for example. The individual signals ŝ_(i)′ may correspond to theindividual destination signals ŝ_(i).

By utilizing the scaled slicer block 362, an estimated value for Q and Icomponents associated with the individual destination signal, ŝ₃, may becomputed based on the value z₃ determined in equation[12b]. The demapperblock 374 may determine a constellation point that corresponds to the Qand I components. Based on the constellation point, a binaryrepresentation may be generated. The binary representation may comprisea binary estimated value for the individual destination signal, ŝ₃. Thedecoder block 376 may decode the binary representation to generatebinary information. The demapper block 374 and/or decoder block 376 mayutilize statistical techniques, for example maximum likelihoodestimation. The encoder block 378 may encode the binary informationdecoded by the decoder block 376. The mapper block 380 may generate Qand I components associated with the constellation point determined bythe demapper block 374. The signal generated by the mapper block 380 maybe referred to as ŝ₃′.

An estimated value for the individual destination signal, ŝ₂, may becomputed based on the value a₂ determined in equation[12c]. The value a₂may be computed based on the estimated value for the individualdestination signal ŝ₃′. The estimated value for the individualdestination signal ŝ₃′, utilized in equation[12c], may be based on Q andI components generated by the mapper block 380. An estimated value forthe individual destination signal, ŝ₁, may be computed based on thevalue z₁ determined in equation[12d]. The value z₁ may be computed basedon the estimated value for the individual destination signals ŝ₂′ andŝ₃′. The estimated values for the individual destination signals ŝ₂′ andŝ₃′, utilized in equation[12c], may be based on Q and I componentsgenerated by the mapper block 380 for the signals ŝ₂′ and ŝ₃′,respectively.

In various embodiments of the invention, the utilization of GMD mayenable the computation of the matrix R wherein each of the matrixelements contained therein may be represented as a real number. This mayreduce the number of computations required at the receiver 352 whendetecting individual signals ŝ_(i) represented by the signal vector Ŝ.When detecting the signals, matrix multiplications may utilize thematrix R and a matrix that comprises one or more matrix elements thatmay be represented as complex numbers. The multiplication of a realnumber and a complex number may involve two multiplication operations.By contrast, for a matrix R that comprises one or more complex elements,multiplication of two complex numbers may involve four multiplicationoperations.

In another aspect of the invention, the values associated with each ofthe diagonal elements in the matrix R may be equal. This may imply thatthe transmitter 302 may utilize equal signal gain when transmitting thespatial streams 306, 308, and 310, for example. This may further implythat the signal strength and/or signal to noise ratio (SNR) measurementsassociated with the transmitted spatial streams may be about equalacross the plurality of transmitted spatial streams. Thus, variousembodiments of the invention that utilize a GMD method may achievehigher information transfer rates, as measured in bits/second, and lowerpacket error rates (PER) for weaker coding rates when compared tosystems that utilize an SVD method. For example, a 5/6 BCC rate mayrepresent a weak coding rate in comparison to a 1/2 BCC rate. The 5/6BCC method may comprise 1 redundant bit for error detection and/orcorrection and 5 information bits in each group of 6 transmitted bits,for example. By comparison, the 1/2 BCC method may comprise 1 redundantbit and 1 information bit in each group of 2 transmitted bits, forexample.

FIG. 4 is an exemplary functional block diagram of transceivercomprising a transmitter and a receiver in a MIMO system, which may beutilized in accordance with an embodiment of the invention. FIG. 4 showsa transceiver comprising a transmitter 400, a receiver 401, a processor440, a baseband processor 442, a plurality of transmitter antennas 415 a. . . 415 n, and a plurality of receiver antennas 417 a . . . 417 n. Thetransmitter 400 may comprise a coding block 402, a puncture block 404,an interleaver block 406, a plurality of mapper blocks 408 a . . . 408n, a plurality of inverse fast Fourier transform (IFFT) blocks 410 a . .. 410 n, a beamforming V matrix block 412, and a plurality of digital toanalog (D to A) conversion and antenna front end blocks 414 a . . . 414n. The receiver 401 may comprise a plurality of antenna front end andanalog to digital (A to D) conversion blocks 416 a . . . 416 n, abeamforming U matrix block 418, a plurality of fast Fourier transform(FFT) blocks 420 a . . . 420 n, a channel estimates block 422, anequalizer block 424, a plurality of demapper blocks 426 a . . . 426 n, adeinterleaver block 428, a depuncture block 430, and a Viterbi decoderblock 432.

The variables V and U* in beamforming blocks 412 and 418 respectivelyrefer to matrices utilized in the beamforming technique. U.S.application Ser. No. 11/052,389 filed Feb. 7, 2005, provides a detaileddescription of Eigenbeamforming, which is hereby incorporated herein byreference in its entirety.

The processor 440 may perform digital receiver and/or transmitterfunctions in accordance with applicable communications standards. Thesefunctions may comprise, but are not limited to, tasks performed at lowerlayers in a relevant protocol reference model. These tasks may furthercomprise the physical layer convergence procedure (PLCP), physicalmedium dependent (PMD) functions, and associated layer managementfunctions. The baseband processor 442 may similarly perform functions inaccordance with applicable communications standards. These functions maycomprise, but are not limited to, tasks related to analysis of datareceived via the receiver 401, and tasks related to generating data tobe transmitted via the transmitter 400. These tasks may further comprisemedium access control (MAC) layer functions as specified by pertinentstandards.

In the transmitter 400, the coding block 402 may transform receivedbinary input data blocks by applying a forward error correction (FEC)technique, for example, binary convolutional coding (BCC). Theapplication of FEC techniques, also known as “channel coding”, mayimprove the ability to successfully recover transmitted data at areceiver by appending redundant information to the input data prior totransmission via an RF channel. The ratio of the number of bits in thebinary input data block to the number of bits in the transformed datablock may be known as the “coding rate”. The coding rate may bespecified using the notation i_(b)/t_(b), where t_(b) represents thetotal number of bits that comprise a coding group of bits, while i_(b)represents the number of information bits that are contained in thegroup of bits t_(b). Any number of bits t_(b)−i_(b) may representredundant bits that may enable the receiver 401 to detect and correcterrors introduced during transmission. Increasing the number ofredundant bits may enable greater capabilities at the receiver to detectand correct errors in information bits. The penalty for this additionalerror detection and correction capability may result in a reduction inthe information transfer rates between the transmitter 400 and thereceiver 401. The invention is not limited to BCC, and any one of aplurality of coding techniques, for example, Turbo coding or low densityparity check (LDPC) coding, may also be utilized.

The puncture block 404 may receive transformed binary input data blocksfrom the coding block 402 and alter the coding rate by removingredundant bits from the received transformed binary input data blocks.For example, if the coding block 402 implemented a 1/2 coding rate, 4bits of data received from the coding block 402 may comprise 2information bits, and 2 redundant bits. By eliminating 1 of theredundant bits in the group of 4 bits, the puncture block 404 may adaptthe coding rate from 1/2 to 2/3. The interleaver block 406 may rearrangebits received in a coding rate-adapted data block from the punctureblock 404 prior to transmission via an RF channel to reduce theprobability of uncorrectable corruption of data due to burst of errors,impacting contiguous bits, during transmission via an RF channel. Theoutput from the interleaver block 406 may also be divided into aplurality of streams where each stream may comprise a non-overlappingportion of the bits from the received coding rate-adapted data block.Therefore, for a given number of bits in the coding rate-adapted datablock, b_(db), a given number of streams from the interleaver block 406,n_(st), and a given number of bits assigned to an individual stream i bythe interleaver block 406, b_(st)(i), the number of bits, b_(db), mayequal the number of bits, b_(st)(i), summed across the n_(st) streams.

For a given number of coded bits before interleaving, b_(db), each bitmay be denoted by an index, k=0, 1 . . . b_(db)−1. The interleaver block406 may assign bits to the first spatial stream, spatial stream 0,b_(st)(0), for bit indexes k=0, n_(st), 2*n_(st), . . . , b_(db)−n_(st).The interleaver block 406 may assign bits to spatial stream 1,b_(st)(1), for bit indexes k=1, n_(st)+1, 2*n_(st)+1, . . . ,b_(db)−n_(st)+1. The interleaver block 406 may assign bits to spatialstream 2, b_(st)(2), for bit indexes k=2, n_(st)+2, 2*n_(st)+2, . . . ,b_(db)−n_(st)+2. The interleaver block 406 may assign bits to spatialstream n_(st), b_(st)(n_(st)), for bit indexes k=n_(st)−1, 2*n_(st)−1,3*n_(st−)1, . . . , b_(db)−1.

The plurality of mapper blocks 408 a . . . 408 n may comprise a numberof individual mapper blocks that is equal to the number of individualstreams generated by the interleaver block 406. Each individual mapperblock 408 a . . . 408 n may receive a plurality of bits from acorresponding individual stream, mapping those bits into a “symbol” byapplying a modulation technique based on a “constellation” utilized totransform the plurality of bits into a signal level representing thesymbol. The representation of the symbol may be a complex quantitycomprising in-phase (I) and quadrature (Q) components. The mapper block408 a . . . 408 n for stream i may utilize a modulation technique to mapa plurality of bits, b_(st)(i), into a symbol.

The beamforming V matrix block 412 may apply the beamforming techniqueto the plurality of symbols, or “spatial modes”, generated from theplurality of mapper blocks 408 a . . . 408 n. The beamforming V matrixblock 412 may generate a plurality of signals where the number ofsignals generated may be equal to the number of transmitting antenna atthe transmitter 400. Each signal in the plurality of signals generatedby the beamforming V block 412 may comprise a weighted sum of at leastone of the received symbols from the mapper blocks 408 a . . . 408 n.

The plurality of IFFT blocks 410 a . . . 410 n may receive a pluralityof signals from the beamforming block 412. Each IFFT block 410 a . . .410 n may subdivide the bandwidth of the RF channel into a plurality ofn sub-band frequencies to implement orthogonal frequency divisionmultiplexing (OFDM), buffering a plurality of received signals equal tothe number of sub-bands. Each buffered signal may be modulated by acarrier signal whose frequency is based on that of one of the sub-bands.Each of the IFFT blocks 410 a . . . 410 n may then independently sumtheir respective buffered and modulated signals across the frequencysub-bands to perform an n-point IFFT thereby generating a composite OFDMsignal.

The plurality of digital (D) to analog (A) conversion and antenna frontend blocks 414 a . . . 414 n may receive the plurality of signalsgenerated by the plurality of IFFT blocks 410 a . . . 410 n. The digitalsignal representation received from each of the plurality of IFFT blocks410 a . . . 410 n may be converted to an analog RF signal that may beamplified and transmitted via an antenna. The plurality of D to Aconversion and antenna front end blocks 414 a . . . 414 n may be equalto the number of transmitting antenna 415 a . . . 415 n. Each D to Aconversion and antenna front end block 414 a . . . 414 n may receive oneof the plurality of signals from the beamforming V matrix block 412 andmay utilize an antenna 415 a . . . 415 n to transmit one RF signal viaan RF channel.

In the receiver 401, the plurality of antenna front end and A to Dconversion blocks 416 a . . . 416 n may receive analog RF signals via anantenna, converting the RF signal to baseband and generating a digitalequivalent of the received analog baseband signal. The digitalrepresentation may be a complex quantity comprising I and Q components.The number of antenna front end and A to D conversion blocks 416 a . . .416 n may be equal to the number of receiving antenna 417 a . . . 417 n.

The plurality of FFT blocks 420 a . . . 420 n may receive a plurality ofsignals from the plurality of antenna front end and A to D conversionblocks 416 a . . . 416 n. The plurality of FFT blocks 420 a . . . 420 nmay be equal to the number of antenna front end and A to D conversionblocks 416 a . . . . 416 n. Each FFT block 420 a . . . 420 n may receivea signal from an antenna front end and A to D conversion block 416 a . .. 416 n, independently applying an n-point FFT technique, anddemodulating the signal by a utilizing a plurality of carrier signalsbased on the n sub-band frequencies utilized in the transmitter 400. Thedemodulated signals may be mathematically integrated over one sub bandfrequency period by each of the plurality of FFT blocks 420 a . . . 420n to extract n symbols contained in each of the plurality of OFDMsignals received by the receiver 401.

The beamforming U* block 418 may apply the beamforming technique to theplurality of signals received from the plurality of FFT blocks 420 a . .. 420 n. The beamforming U* block 418 may generate a plurality ofsignals where the number of signals generated may be equal to the numberof spatial streams utilized in generating the signals at the transmitter400. Each of the plurality of signals generated by the beamforming U*block 418 may comprise a weighted sum of at least one of the signalsreceived from the FFT blocks 420 a . . . 420 n.

The channel estimates block 422 may utilize preamble information,contained in a received RF signal, to compute channel estimates. Theequalizer block 424 may receive signals generated by the beamforming U*block 418. The equalizer block 424 may process the received signalsbased on input from the channel estimates block 422 to recover thesymbol originally generated by the transmitter 400. The equalizer block424 may comprise suitable logic, circuitry, and/or code that may enabletransformation of symbols received from the beamforming U* block 418 tocompensate for fading in the RF channel.

The plurality of demapper blocks 426 a . . . 426 n may receive symbolsfrom the equalizer block 424, reverse mapping each symbol to one or morebinary bits by applying a demodulation technique, based on themodulation technique utilized in generating the symbol at thetransmitter 400. The plurality of demapper blocks 426 a . . . 426 n maybe equal to the number of streams in the transmitter 400.

The deinterleaver block 428 may receive a plurality of bits from each ofthe demapper blocks 426 a . . . 426 n, rearranging the order of bitsamong the received plurality of bits. The deinterleaver block 428 mayrearrange the order of bits from the plurality of demapper blocks 426 a. . . 426 n in, for example, the reverse order of that utilized by theinterleaver 406 in the transmitter 400. The depuncture block 430 mayinsert “null” bits into the output data block received from thedeinterleaver block 428 that were removed by the puncture block 404. TheViterbi decoder block 432 may decode a depunctured output data block,applying a decoding technique that may recover the binary data blocksthat were input to the coding block 402.

In operation, the processor 440 may receive decoded data from theViterbi decoder 432. The processor 440 may communicate received data tothe baseband processor 442 for analysis and further processing. Theprocessor 440 may also communicate data received via the RF channel, bythe receiver 401, to the channel estimates block 422. This informationmay be utilized by the channel estimates block 422, in the receiver 401,to compute channel estimates for a received RF channel. The basebandprocessor 442 may generate data to be transmitted via an RF channel bythe transmitter 400. The baseband processor 442 may communicate the datato the processor 440. The processor 440 may generate a plurality of bitsthat are communicated to the coding block 402.

The elements shown in FIG. 4 may comprise components that may be presentin an exemplary embodiment of a wireless communications terminal. Oneexemplary embodiment of a may be a wireless communications transmittercomprising a transmitter 400, a processor 440, and a baseband processor442. Another exemplary embodiment of a may be a wireless communicationsreceiver comprising a receiver 401, a processor 440, and a basebandprocessor 442. Another exemplary embodiment of a may be a wirelesscommunications transceiver comprising a transmitter 400, a receiver 401,a processor 440, and a baseband processor 442.

U.S. application Ser. No. 11/372,752 provides further details about RFchannels utilized in MIMO communications and the construction of thefeedback matrix V and is hereby incorporation in its entirety.

The Givens rotation may be represented as an N×N Givens rotation matrix,G_(li)(ψ), in the following expression:

$\begin{matrix}{{G_{li}\left( \psi_{li} \right)} = \begin{bmatrix}I_{1 - i} & 0 & 0 & 0 & 0 \\0 & {\cos\left( \psi_{li} \right)} & 0 & {\sin\left( \psi_{li} \right)} & 0 \\0 & 0 & I_{i - l - 1} & 0 & 0 \\0 & {- {\sin\left( \psi_{li} \right)}} & 0 & {\cos\left( \psi_{li} \right)} & 0 \\0 & 0 & 0 & 0 & I_{N - i}\end{bmatrix}} & {{equation}\mspace{14mu}\lbrack 13\rbrack}\end{matrix}$where I may indicate a row in a matrix, i may indicate a column, I_(n)may represent an identity matrix comprising n rows and n columns, andψ_(li) may represent a rotation angle. The value of the element locatedat the I^(th) row and I^(th) column in the matrix of equation[13] may beabout equal to the value of the expression cos(ψ_(li)). The value of theelement located at the i^(th) row and i^(th) column may be about equalto the value of the expression cos(ψ_(li)). The value of the elementlocated at the I^(th) row and i_(th) column may be about equal to thevalue of the expression −sin(ψ_(li)). The value of the element locatedat the i^(th) row and I^(th) column may be about equal to the value ofthe expression sin(ψ_(li)). Each “0” indicated in the matrix ofequation[13] may represent one or more matrix elements for which eachcorresponding value is about 0. For example, the first row of 0's in thematrix may represent a block of elements comprising I-1 rows and N-(I-1)columns for which the value of each element is about 0. A block ofelements comprising 0 rows and/or 0 columns may be omitted from thematrix of equation[13].

A steering matrix may be utilized to rotate elements in a matrix suchthat at least a portion of the rotated elements are represented as realnumbers. A matrix, {tilde under (V)}, may comprise elements that may berepresented as complex numbers. The matrix {tilde under (V)} may bemultiplied by an M×M column-wise steering matrix {tilde under (D)} whichmay be represented as follows:

$\begin{matrix}{\underset{\sim}{D} = \begin{bmatrix}{\mathbb{e}}^{{j\theta}_{1}} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}} & 0 & \vdots \\\vdots & 0 & \ddots & 0 \\0 & \ldots & 0 & {\mathbb{e}}^{{j\theta}_{M}}\end{bmatrix}} & {{equation}\mspace{14mu}\lbrack 14\rbrack}\end{matrix}$where θ_(i) may represent a phase shift associated with column i, e mayrepresent a value about equal to 2.718, and j may represent the complexvalue equal to the square root of −1.

In an exemplary embodiment of the invention, the values for the phaseshifts θ_(i) in equation[14] may be selected such that the matrixelements in the last row in a matrix representing the matrixmultiplication product {tilde under (V)}×{tilde under (D)} may each berepresented as a real number. The matrix V may be computed based on thematrix multiplication product {tilde under (V)}×{tilde under (D)} andthe matrix P, as shown in equation[7a]

The matrix V may be multiplied by an N×N phase rotation matrix, D_(i),which may be represented as follows:

$\begin{matrix}{D_{i} = \begin{bmatrix}I_{i - 1} & 0 & \ldots & \; & 0 \\0 & {\mathbb{e}}^{{j\varphi}_{i,i}} & 0 & \; & \; \\\vdots & 0 & \ddots & \; & \vdots \\\; & \; & \; & {\mathbb{e}}^{{j\varphi}_{{N - 1},i}} & \; \\0 & \ldots & \; & \; & 1\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {15a} \right\rbrack}\end{matrix}$where φ_(a,b) may represent a phase shift associated with a matrixelement located at row a and column b in the matrix V. For example aphase rotation D₁ matrix may be represented as follows:

$\begin{matrix}{D_{i} = \begin{bmatrix}{\mathbb{e}}^{{j\varphi}_{1,1}} & 0 & \ldots & \; & 0 \\0 & {\mathbb{e}}^{{j\varphi}_{2,1}} & 0 & \; & \; \\\vdots & 0 & \ddots & \; & \vdots \\\; & \; & \; & {\mathbb{e}}^{{j\varphi}_{{N - 1},i}} & \; \\0 & \ldots & \; & \; & 1\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {15b} \right\rbrack}\end{matrix}$

The result of the matrix multiplication of the matrix V by the phaserotation matrix D_(i)* may result in a phase shifted version of thematrix V, where D_(i)* may represent an Hermitian transpose of the phaseshift matrix D_(i). For example, the matrix product D₁*V may berepresented as a matrix in which the values associated with elements inthe first column may each be represented as a real number.

The matrix product G_(li)(ψ_(li))D_(i)*V may represent a Givens rotatedversion of the matrix that represents the matrix product D_(i)*V. If anonzero value is associated with an element located in the I^(th) rowand i^(th) column of the matrix that represents the matrix productD_(i)*V, represented as the (l,i) element, the corresponding value ofthe (l,i) element of the matrix that represents the matrix productG_(li)(ψ_(li))D_(i)*V may be about equal to 0.

One characteristic of Givens rotations is that rotations may be appliediteratively to select matrix elements for which corresponding values areto be set to about 0 as a result of successive rotations. For example,based on a current Givens rotation matrix, G_(li)(ψ_(li)), and asubsequent Givens matrix G_(ki)(ψ_(ki)), a subsequent matrix productG_(li)(ψ_(li))G_(ki)(ψ_(ki))D_(i)*V may be computed. The value of the(l,i) element of the matrix that represents the subsequent matrixproduct may be equal to about 0. The value of the (k,i) element of thematrix that represents the subsequent matrix product may also be aboutequal to 0.

In various embodiments of the invention, the process may be repeateduntil a subsequent rotated matrix is computed such that the valueassociated with each element I in column i is about equal to 0. Therange of values for the row indicator I may be subject to the followingcondition:N≧1>i  equation[16]where N may represent the number of rows in the matrix V.

After repeating the process for each element I in column i=1, forexample, a subsequent rotated matrix may be represented as follows:

$\begin{matrix}{{{G_{N\; 1}\left( \psi_{N\; 1} \right)}\ldots\mspace{11mu}{G_{31}\left( \psi_{31} \right)}{G_{21}\left( \psi_{21} \right)}D_{1}^{*}V} = \begin{bmatrix}1 & 0 & \ldots & 0 \\0 & \; & \; & \; \\\vdots & V_{2} & \; & \; \\0 & \; & \; & \;\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {17a} \right\rbrack}\end{matrix}$where V₂ may represent an (N−1)×(M−1) submatrix.

For i=2, a submatrix V₃ may be computed as follows:

$\begin{matrix}{\begin{matrix}\left( {{G_{N\; 2}\left( \psi_{N\; 2} \right)}\ldots\mspace{11mu}{G_{42}\left( \psi_{32} \right)}{G_{32}\left( \psi_{22} \right)}D_{2}^{*}} \right) \\{\left( {{G_{N\; 1}\left( \psi_{N\; 2} \right)}\ldots\mspace{11mu}{G_{31}\left( \psi_{31} \right)}{G_{21}\left( \psi_{21} \right)}D_{1}^{*}} \right)V}\end{matrix} = \begin{bmatrix}1 & 0 & \ldots & 0 \\0 & \; & \; & \; \\\vdots & V_{2} & \; & \; \\0 & \; & \; & \;\end{bmatrix}} & {{equation}\mspace{14mu}\left\lbrack {17b} \right\rbrack}\end{matrix}$

For an i^(th) column, equation[17a] may be generalized and representedas follows:

$\begin{matrix}{\begin{matrix}{{G_{N,1}\left( \psi_{N\; 1} \right)}\ldots\mspace{11mu}{G_{{i + 2},i}\left( \psi_{31} \right)}} \\{{G_{{i + 1},i}\left( \psi_{21} \right)}D_{i}^{*}R_{i}}\end{matrix} = \begin{bmatrix}I_{i} & 0 & \ldots & 0 \\0 & \; & \; & \; \\\vdots & V_{i + 1} & \; & \; \\0 & \; & \; & \;\end{bmatrix}} & {{equation}\mspace{14mu}\lbrack 18\rbrack}\end{matrix}$where R_(i) may represent an intermediate rotated matrix thatcorresponds to an identity matrix I_(i-1), and a submatrix V_(i). Thesubmatrix V_(i+1) may represent an (N−i)×(M−i) submatrix. For example,in equation[17b] the intermediate rotated matrix R₂ may be representedby the matrix product (G_(N1)(ψ_(N2)) . . . G₃₁(ψ₃₁) G₂₁(ψ₂₁)D₁*)V.

In various embodiments of the invention, the process shown inequation[18] may be repeated for a subsequent column wherein the rangeof values for the column indicator i may be subject to the followingcondition:min(M,N−1)≧i≧1  equation[19]where N may represent the number of rows in the matrix V, M mayrepresent the number of columns in the matrix V, and min(a,b) mayrepresent an expression, the value of which may be the minimum valueamong arguments a and b.

Based on equations [13], [15a], [18], [19], and the unitary matrixproperty, the matrix V may be expressed based the Givens rotationsaccording to the following equation:

$\begin{matrix}{V = {\prod\limits_{i = 1}^{\min{({M,{N - 1}})}}{\left\lbrack {D_{i}{\prod\limits_{l = {i + 1}}^{N}{G_{li}^{*}\left( \psi_{li} \right)}}} \right\rbrack \times \overset{\sim}{I}}}} & {{equation}\mspace{14mu}\lbrack 20\rbrack}\end{matrix}$where Ĩ may represent an N×M matrix comprising an identity matrixI_(min(N,M)) and either a block of max(0,N−M) rows of elements, or ablock of max(0,M−N) columns of elements, with each element of a valueabout 0, max(a,b) may represent an expression, the value of which may bethe maximum value among arguments a and b, and the operator π[X_(i)] mayrepresent a right-side matrix multiplication product among a set ofmatrices X_(i). G_(li)(ψ_(li))* may represent an Hermitian transpose ofthe Givens rotation matrix G_(li)(ψ_(li)). The Givens rotation matrixG_(li)(ψ_(li)) is as defined in equation[13] and the phase shift matrixD_(i) is as defined in equation[15a].

In various embodiments of the invention, feedback information maycomprise values for one or more rotation angle parameters comprising oneor more phase shift angles ψ_(li) and one or more Givens rotation anglesψ_(li). The following table represents the number of parameters that maybe utilized in feedback information to represent an N×M beamformingmatrix V, for exemplary values of N rows and M columns:

Angles to be reported in feedback information Dimensions Number of (N ×M) Parameters Feedback Angle Parameters 2 × 1 2 φ₁₁, ψ₂₁ 2 × 2 2 φ₁₁,ψ₂₁ 3 × 1 4 φ₁₁, φ₂₁, ψ₂₁, ψ₃₁ 3 × 2 6 φ₁₁, φ₂₁, ψ₂₁, ψ₃₁, φ₂₂, ψ₃₂ 3 ×3 6 φ₁₁, φ₂₁, ψ₂₁, ψ₃₁, φ₂₂, ψ₃₂ 4 × 1 6 φ₁₁, φ₂₁, φ₃₁, ψ₂₁, ψ₃₁, ψ₄₁ 4× 2 10 φ₁₁, φ₂₁, φ₃₁, ψ₂₁, ψ₃₁, ψ₄₁, φ₂₂, φ₃₂, ψ₃₂, ψ₄₂ 4 × 3 12 φ₁₁,φ₂₁, φ₃₁, ψ₂₁, ψ₃₁, ψ₄₁, φ₂₂, φ₃₂, ψ₃₂, ψ₄₂, φ₃₃, ψ₄₃ 4 × 4 12 φ₁₁, φ₂₁,φ₃₁, ψ₂₁, ψ₃₁, ψ₄₁, φ₂₂, φ₃₂, ψ₃₂, ψ₄₂, φ₃₃, ψ₄₃

The feedback angles represented in Table 1 may be reported for each ofthe N_(sc) plurality of frequency subcarriers associated with thecorresponding downlink RF channel. The order of angles represented inTable 1 may be determined based on the order of multiplications that maybe performed when reconstructing the V matrix for each subcarrier at theWLAN 106 that receives the feedback information. For example, for givenfeedback angles, φ_(li) and ψ_(li), the angles may be represented as avectors of angles, φ_(li)[−N_(sc)/2, −N_(sc)/2+1, . . . , −2, −1, 1, 2,. . . , N_(sc)/2−1, N_(sc)/2] and ψ_(li)[−N_(sc)/2, −N_(sc)/2+1, . . . ,−2, −1, 1, 2, . . . , N_(sc)/2−1, N_(sc)/2], where N_(sc) may representthe number of subcarriers associated with the downlink RF channel.

In various embodiments of the invention, the order in which feedbackangles φ_(li) and ψ_(li) may be reported as shown in Table 1 isexemplary, the feedback angles may be reported based on other orderings.In an exemplary embodiment of the invention, which utilizes a 4×2beamforming matrix V, the order in which feedback angles may be reportedmay be represented φ₁₁, φ₂₁, ψ₂₁, φ₂₂, φ₃₁, ψ₃₁, φ₄₁, ψ₄₁, φ₃₂, ψ₃₂, andψ₄₂.

Actual values for angles reported in feedback information may bedetermined based on a codebook. For example, a range of true values forGivens rotation angles may comprise 0≦ψ_(li)≦π/2. A range of true valuesfor phase rotation angles may comprise 0≦φ_(li)≦2π, for example. Valuesfor the Givens rotation angles may be approximated based on a binaryencoding comprising a plurality of b_(ψ) bits. Values for Givensrotation angles that are represented by a binary encoding of bits may bereferred to as quantized values. In one embodiment of the invention, therange of values for binary quantized values for the Givens rotationangles may comprise kπ/2^(b) ^(ψ) ⁺¹+π/2^(b) ^(ψ) ⁺², where k may beequal to one of a range of values comprising 0, 1, . . . , 2^(b) ^(ψ)−1, for example. Values for the phase rotation angles may beapproximated based on a binary encoding comprising a plurality of b_(φ)bits. In an embodiment of the invention, the range of values for binaryquantized values for the phase rotation angles may comprise kπ/2^(b)^(φ) ⁻¹, where k may be equal to one of a range of values comprising 0,1, . . . , 2^(b) ^(φ) −1, for example. Differences in value between atrue value and a corresponding quantized value may be referred to as aquantization error. The potential size of a given quantization error maybe based on the number of bits utilized during binary encoding.

The number of bits utilized during binary encoding of ψ_(li) and duringbinary encoding of φ_(li) respectively may be represented as a (b_(ψ),b_(φ)) tuple. A tuple utilized in an exemplary codebook may comprise(1,3) to represent the combination b_(ψ)=1 and b_(φ)=3. Other tuples inthe exemplary codebook may comprise (2,4), (3,5), or (4,6).

Table 2A presents an exemplary mapping between bits contained infeedback information, and the corresponding angle that may be reported.In Table 2A, N=2, M=2, the downlink channel may be a 20 MHz RF channel,and the bits utilized may be represented by (3,5). The range b_(j) . . .b_(k) may represent a range of bit positions in the feedback informationwhere in b_(j) may represent the least significant bit (LSB) in therange and b_(k) may represent the most significant bit (MSB) in therange, for example. The notation f_(p) may represent a frequencysubcarrier associated with the RF channel. Values for the index p mayrepresent a range of integer values as determined in equations [15a] and[16]. The notation ψ_(li)(f_(p)) may refer to a Givens rotation angleassociated with frequency subcarrier f_(p). The notation φ_(li)(f_(p))may refer to a phase rotation angle associated with frequency subcarrierf_(p).

TABLE 2A Exemplary encoding of feedback information for 20 MHz ChannelFeedback Bits Angle Reported b₁ . . . b₅ φ₁₁(f⁻²⁸) b₆ . . . b₁₀φ₁₁(f⁻²⁷) . . . . . . b₂₇₆ . . . b₂₈₀ φ₁₁(f₂₈) b₂₈₁ . . . b₂₈₃ ψ₂₁(f⁻²⁸)b₂₈₄ . . . b₂₈₆ ψ₂₁(f⁻²⁷) . . . . . . b₄₄₆ . . . b₄₄₈ ψ₂₁(f₂₈)

The exemplary feedback information shown in Table 2A contains 448 bits:168 bits may be utilized to communicate Givens rotation angles, and 280bits may be utilized to communicate phase rotation angles.

Various embodiments of the invention may also be utilized with tonegrouping methods. U.S. application Ser. No. 11/372,752 describes tonegrouping methods and is hereby incorporated herein in its entirety.

The order in which feedback angles φ_(li) and φ_(li) may be encoded asshown in Table 2A is exemplary, the feedback angles may be reportedbased on other orderings. Table 2B presents an exemplary mapping betweenbits contained in feedback information, in which the feedback angles maybe grouped by frequency for a 20 MHz RF channel, and for a 4×2beamforming matrix V.

TABLE 2B Exemplary encoding of explicit feedback information for 20 MHzChannel Feedback Bits Angle Reported b₁ . . . b₄ φ₂₁(f⁻²⁸) b₅ . . . b₈φ₃₁(f⁻²⁸) b₉ . . . b₁₂ φ₄₁(f⁻²⁸) b₁₃ . . . b₁₄ ψ₂₁(f⁻²⁸) b₁₅ . . . b₁₆ψ₃₁(f⁻²⁸) b₁₇ . . . b₁₈ ψ₄₁(f⁻²⁸) b₁₉ . . . b₂₂ φ₃₂(f⁻²⁸) b₂₃ . . . b₂₆φ₄₂(f⁻²⁸) b₂₇ . . . b₂₈ ψ₃₂(f⁻²⁸) b₂₉ . . . b₃₀ ψ₄₂(f⁻²⁸) . . . . . .

Table 3A presents an exemplary mapping between bits contained infeedback information, and the corresponding angle that may be reported.In Table 3A, N=2, M=4, the downlink channel may be a 40 MHz RF channel,and the bits utilized may be represented by (2,4). The tone groupingsize may be represented by ε=4. The range b_(j) . . . b_(k) mayrepresent a range of bit positions in the feedback information where inb_(j) may represent the least significant bit (LSB) in the range andb_(k) may represent the most significant bit (MSB) in the range, forexample. The notation f_(p) may represent a frequency subcarrierassociated with the RF channel. The notation ψ_(li)(f_(p)) may refer toa Givens rotation angle associated with frequency subcarrier f_(p). Thenotation φ_(li)(f_(p)) may refer to a phase rotation angle associatedwith frequency subcarrier f_(p).

TABLE 3A Exemplary encoding of feedback information for 40 MHz ChannelFeedback Bits Angle Reported b₁ . . . b₄ φ₁₁(f⁻⁵⁶) . . . . . . b₁₁₃ . .. b₁₁₆ φ₂₁(f⁻⁵⁶) . . . . . . b₃₃₇ . . . b₃₃₈ ψ₂₁(f⁻⁵⁶) . . . . . . b₅₀₅. . . b₅₀₈ φ₂₂(f⁻⁵⁶) . . . . . . b₈₃₉ . . . b₈₄₀ ψ₄₂(f₅₆)

The exemplary feedback information shown in Table 3A contains 840 bits:280 bits may be utilized to communicate Givens rotation angles, and 560bits may be utilized to communicate phase rotation angles.

The order in which feedback angles φ_(li) and ψ_(li) may be encoded asshown in Table 3A is exemplary, the feedback angles may be reportedbased on other orderings. Table 3B presents an exemplary mapping betweenbits contained in feedback information, in which the feedback angles maybe grouped by frequency for a 40 MHz channel.

TABLE 3B Exemplary encoding of explicit feedback information for 40 MHzChannel Feedback Bits Angle Reported b₁ . . . b₄ φ₂₁(f⁻⁵⁶) b₅ . . . b₈φ₃₁(f⁻⁵⁶) b₉ . . . b₁₂ φ₄₁(f⁻⁵⁶) b₁₃ . . . b₁₄ ψ₂₁(f⁻⁵⁶) b₁₅ . . . b₁₆ψ₃₁(f⁻⁵⁶) b₁₇ . . . b₁₈ ψ₄₁(f⁻⁵⁶) b₁₉ . . . b₂₂ φ₃₂(f⁻⁵⁶) b₂₃ . . . b₂₆φ₄₂(f⁻⁵⁶) b₂₇ . . . b₂₈ ψ₃₂(f⁻⁵⁶) b₂₉ . . . b₃₀ ψ₄₂(f⁻⁵⁶) . . . . . .b₈₁₁ . . . b₈₁₄ φ₂₁(f₅₆) b₈₁₅ . . . b₈₁₈ φ₃₁(f₅₆) b₈₁₉ . . . b₈₂₂φ₄₁(f₅₆) b₈₂₃ . . . b₈₂₄ ψ₂₁(f₅₆) b₈₂₅ . . . b₈₂₆ ψ₃₁(f₅₆) b₈₂₇ . . .b₈₂₈ ψ₄₁(f₅₆) b₈₂₉ . . . b₈₃₂ φ₃₂(f₅₆) b₈₃₃ . . . b₈₃₆ φ₄₂(f₅₆) b₈₃₇ . .. b₈₃₈ ψ₃₂(f₅₆) b₈₃₉ . . . b₈₄₀ ψ₄₂(f₅₆)

U.S. application Ser. No. 11/372,752 further details exemplary numbersof bytes contained in feedback information in accordance with variousembodiments of the invention and is hereby incorporation in itsentirety.

FIG. 5 is a flowchart illustrating exemplary steps for computingquantization for a general beamforming matrix in feedback information,in accordance with an embodiment of the invention. Referring to FIG. 5,in step 502, a signal Y may be received at a receiving mobile terminal322. In step 504, a channel estimate matrix H may be computed. In step506, the computed channel estimate matrix may be decomposed into amatrix multiplication representation, H=URV*. In step 508, the matrix Vmay be computed such that the matrix R is a real valued upper diagonalmatrix. A matrix may be referred to as being real valued when each ofthe matrix elements contained within the matrix may be represented as areal number. The values of each of the diagonal matrix elements in thematrix R, r_(ii), may be about equal. In step 510, the receiving mobileterminal 322 may send feedback information based on the computed matrixV to the transmitting mobile terminal 302 via an uplink channel.

FIG. 6 is a flowchart illustrating exemplary steps for utilizingquantization for a general beamforming matrix in feedback information,in accordance with an embodiment of the invention. Referring to FIG. 6,in step 602, a transmitting mobile terminal 302 may receive feedbackinformation. In step 604, beamforming parameters may be adjusted basedon the feedback information. In step 606, the transmitting mobileterminal 302 may transmit spatial streams. Each spatial stream may betransmitted with approximately equal signal gain based on the feedbackinformation. Each transmitted spatial stream may be characterized byapproximately equal signal strength and/or signal to noise ratio (SNR)measurements. The signal strength and/or SNR may be measured in decibels(dB), for example.

Various embodiments of the invention may not be limited to geometricmean decomposition (GMD) but may comprise other methods that may beutilized at a receiving mobile terminal 322 to compute feedbackinformation based on a signal Y, received via a downlink channel. Thereceived signal may be utilized to compute a channel estimate matrix H.The channel estimate matrix H may be decomposed into a matrixmultiplication representation H=URV*. The matrix V may be computed suchthat the matrix R is an upper diagonal real valued matrix with equalvalued diagonal matrix elements. The receiving mobile terminal 322 maysend feedback information, based on the computed matrix V, to atransmitting mobile terminal 302 via an uplink channel. The receivingmobile terminal may utilize the feedback information to beamform asubsequent transmitted signal vector X. The signal vector X may comprisea plurality of transmitted spatial streams. For each transmitted spatialstream in the beamformed subsequent signal vector X, a signal strengthand/or SNR measurement may be about equal to corresponding measurementsassociated with each of the other transmitted spatial streams.

Aspects of a system for processing signals in a communication system maycomprise a processor 282 that enables receipt of a matrix for a wirelessmedium, which comprises a multiplicative product of at least onerotation matrix and at least one diagonal phase rotation matrix. Each ofthe rotation matrices comprises at least one matrix element whose valueis based on a Givens rotation angle. The system may also comprise atransmitter 286 that enables transmission of a plurality of signals viathe wireless medium based on feedback information. A signal strengthand/or signal to noise ratio (SNR) measurement associated with each ofthe plurality of signals may be about equal.

A value associated with each matrix element in a last row of thereceived matrix may be represented as a real number. The processor 282may enable computation of a phase rotated matrix by multiplying thereceived matrix by a diagonal phase rotation matrix. A value associatedwith each matrix element in a first column of the phase rotated matrixmay be represented as a real number. The processor 282 may enablecomputation of a product matrix based on a multiplicative product of thephase rotated matrix and at least one phase rotation matrix. Each of theone or more phase rotation matrices may comprise at least one matrixelement the value of which may be based on a Givens rotation angle. Theproduct matrix may comprise an identity matrix and a second matrix. Thesecond matrix may comprise one row and one column less than the receivedmatrix.

The processor 282 may enable computation of a subsequent product matrixbased on a multiplicative product of the received matrix, at least onediagonal phase rotation matrix, and at least one phase rotation matrix.The processor 282 may enable computation of a phase rotated intermediatematrix by multiplying an intermediate matrix by a corresponding one ofthe one or more diagonal phase rotation matrices. A value associatedwith each matrix element in a corresponding column of the phase rotatedintermediate matrix may be represented as a real number. The subsequentproduct matrix may comprise an identity matrix and a subsequent matrix.The subsequent matrix may comprise at least one row and at least onecolumn less than the received matrix.

Accordingly, the present invention may be realized in hardware,software, or a combination of hardware and software. The presentinvention may be realized in a centralized fashion in at least onecomputer system, or in a distributed fashion where different elementsare spread across several interconnected computer systems. Any kind ofcomputer system or other apparatus adapted for carrying out the methodsdescribed herein is suited. A typical combination of hardware andsoftware may be a general-purpose computer system with a computerprogram that, when being loaded and executed, controls the computersystem such that it carries out the methods described herein.

The present invention may also be embedded in a computer programproduct, which comprises all the features enabling the implementation ofthe methods described herein, and which when loaded in a computer systemis able to carry out these methods. Computer program in the presentcontext means any expression, in any language, code or notation, of aset of instructions intended to cause a system having an informationprocessing capability to perform a particular function either directlyor after either or both of the following: a) conversion to anotherlanguage, code or notation; b) reproduction in a different materialform.

While the present invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the present invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the present invention without departing from its scope.Therefore, it is intended that the present invention not be limited tothe particular embodiment disclosed, but that the present invention willinclude all embodiments falling within the scope of the appended claims.

What is claimed is:
 1. A method for processing signals in acommunication system, the method comprising: receiving a matrix for awireless medium, which comprises a multiplicative product of at leastone rotation matrix and at least one diagonal phase rotation matrix,wherein each of said at least one rotation matrix comprises at least onematrix element whose value is based on a Givens rotation angle; andtransmitting a plurality of signals via said wireless medium based onfeedback information, wherein a signal to noise ratio (SNR) measurementassociated with each of said plurality of signals is substantiallyequal.
 2. The method according to claim 1, wherein a value associatedwith each matrix element in a last row of said received matrix isrepresented as a real number.
 3. The method according to claim 2,further comprising computing a phase rotated matrix by multiplying saidreceived matrix by a diagonal phase rotation matrix.
 4. The methodaccording to claim 3, wherein a value associated with each matrixelement in a first column of said phase rotated matrix is represented asa real number.
 5. The method according to claim 4, further comprisingcomputing a product matrix based on a multiplicative product of saidphase rotated matrix and at least one phase rotation matrix.
 6. Themethod according to claim 5, wherein each of said at least one phaserotation matrix comprises at least one matrix element the value of whichis based on a Givens rotation angle.
 7. The method according to claim 5,wherein said product matrix comprises an identity matrix and a secondmatrix.
 8. The method according to claim 7, wherein said second matrixcomprises one row and one column less than said received matrix.
 9. Themethod according to claim 1, further comprising computing a subsequentproduct matrix based on a multiplicative product of said receivedmatrix, at least one diagonal phase rotation matrix, and at least onephase rotation matrix.
 10. The method according to claim 9, furthercomprising computing a phase rotated intermediate matrix by multiplyingan intermediate matrix by a corresponding one of said at least onediagonal phase rotation matrix.
 11. The method according to claim 10,wherein a value associated with each matrix element in a correspondingcolumn of said phase rotated intermediate matrix is represented as areal number.
 12. The method according to claim 9, wherein saidsubsequent product matrix comprises an identity matrix and a subsequentmatrix.
 13. The method according to claim 12, wherein said subsequentmatrix comprises at least one row and at least one column less than saidreceived matrix.
 14. A system for processing signals in a communicationsystem, the system comprising: a processor that enables receipt of amatrix for a wireless medium, which comprises a multiplicative productof at least one rotation matrix and at least one diagonal phase rotationmatrix, wherein each of said at least one rotation matrix comprises atleast one matrix element whose value is based on a Givens rotationangle; and a transmitter that enables transmission of a plurality ofsignals via said wireless medium based on feedback information, whereina signal to noise ratio (SNR) measurement associated with each of saidplurality of signals is substantially equal.
 15. The system according toclaim 14, wherein a value associated with each matrix element in a lastrow of said received matrix is represented as a real number.
 16. Thesystem according to claim 15, wherein said processor enables computationof a phase rotated matrix by multiplying said received matrix by adiagonal phase rotation matrix.
 17. The system according to claim 16,wherein a value associated with each matrix element in a first column ofsaid phase rotated matrix is represented as a real number.
 18. Thesystem according to claim 17, wherein said processor enables computationof a product matrix based on a multiplicative product of said phaserotated matrix and at least one phase rotation matrix.
 19. The systemaccording to claim 18, wherein each of said at least one phase rotationmatrix comprises at least one matrix element the value of which is basedon a Givens rotation angle.
 20. The system according to claim 18,wherein said product matrix comprises an identity matrix and a secondmatrix.
 21. The system according to claim 20, wherein said second matrixcomprises one row and one column less than said received matrix.
 22. Thesystem according to claim 14, wherein said processor enables computationof a subsequent product matrix based on a multiplicative product of saidreceived matrix, at least one diagonal phase rotation matrix, and atleast one phase rotation matrix.
 23. The system according to claim 22,wherein said processor enables computation of an phase rotatedintermediate matrix by multiplying an intermediate matrix by acorresponding one of said at least one diagonal phase rotation matrix.24. The system according to claim 23, wherein a value associated witheach matrix element in a corresponding column of said phase rotatedintermediate matrix is represented as a real number.
 25. The systemaccording to claim 22, wherein said subsequent product matrix comprisesan identity matrix and a subsequent matrix.
 26. The system according toclaim 25, wherein said subsequent matrix comprises at least one row andat least one column less than said received matrix.